On the Eigenspaces of Lamplighter Random Walks and Percolation Clusters on Graphs
Functional Analysis
2012-12-06 v2 Probability
Abstract
We show that the Plancherel measure of the lamplighter random walk on a graph coincides with the expected spectral measure of the absorbing random walk on the Bernoulli percolation clusters. In the subcritical regime the spectrum is pure point and we construct a complete orthonormal basis of finitely supported eigenfunctions.
Cite
@article{arxiv.0805.0867,
title = {On the Eigenspaces of Lamplighter Random Walks and Percolation Clusters on Graphs},
author = {Franz Lehner},
journal= {arXiv preprint arXiv:0805.0867},
year = {2012}
}
Comments
notational improvements and minor corrections, 6 pages; complement to arXiv:0712.3135